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I broadcast last year and it did work, but the problem was weeding. Its far easier with a hoe so you can go down the lines. Its a 'kneel down and get your hands dirty' job when you broadcast them.
In my personal opinion I find both broadcast sowing and row sowing to very untidy and wasteful.To sow carrots I use seed dots(similar to seed tape but only one seed per 1 cm square pieces) sown in blocks or offset blocked rows, in both methods I use a drilled wooden template.